diff --git a/tests/keras_tests/function_tests/test_hmse_error_method.py b/tests/keras_tests/function_tests/test_hmse_error_method.py
index c217b4c95..1b1fed1ce 100644
--- a/tests/keras_tests/function_tests/test_hmse_error_method.py
+++ b/tests/keras_tests/function_tests/test_hmse_error_method.py
@@ -165,44 +165,11 @@ def test_uniform_threshold_selection_hmse_per_tensor(self):
         self._verify_params_calculation_execution(RANGE_MAX)
 
     def test_threshold_selection_hmse_no_gptq(self):
-        self._setup_with_args(quant_method=mct.target_platform.QuantizationMethod.SYMMETRIC, per_channel=True,
-                              running_gptq=False)
-
-        def _verify_node_default_mse_error(node_type):
-            node = [n for n in self.graph.nodes if n.type == node_type]
-            self.assertTrue(len(node) == 1, f"Expecting exactly 1 {node_type} node in test model.")
-            node = node[0]
-
-            kernel_attr_error_method = (
-                node.candidates_quantization_cfg[0].weights_quantization_cfg.get_attr_config(KERNEL).weights_error_method)
-            self.assertTrue(kernel_attr_error_method == mct.core.QuantizationErrorMethod.MSE,
-                            f"Expecting {node_type} node quantization parameter error method to be the default "
-                            f"MSE when not running with GPTQ, but is set to {kernel_attr_error_method}.")
-
-        # verifying that the nodes quantization params error method is changed to the default MSE
-        _verify_node_default_mse_error(layers.Conv2D)
-        _verify_node_default_mse_error(layers.Dense)
-
-        calculate_quantization_params(self.graph, fw_impl=self.keras_impl, repr_data_gen_fn=representative_dataset,
-                                      hessian_info_service=self.his, num_hessian_samples=1)
-
-        def _verify_node_no_hessian_computed(node_type):
-            node = [n for n in self.graph.nodes if n.type == node_type]
-            self.assertTrue(len(node) == 1, f"Expecting exactly 1 {node_type} node in test model.")
-            node = node[0]
-
-            expected_hessian_request = HessianScoresRequest(mode=HessianMode.WEIGHTS,
-                                                            granularity=HessianScoresGranularity.PER_ELEMENT,
-                                                            data_loader=None,
-                                                            n_samples=1,
-                                                            target_nodes=[node])
-
-            with self.assertRaises(ValueError, msg='Not enough hessians are cached to fulfill the request') as e:
-                self.his.fetch_hessian(expected_hessian_request)
-
-        # verifying that no Hessian scores were computed
-        _verify_node_no_hessian_computed(layers.Conv2D)
-        _verify_node_no_hessian_computed(layers.Dense)
+        with self.assertRaises(ValueError) as e:
+            self._setup_with_args(quant_method=mct.target_platform.QuantizationMethod.SYMMETRIC, per_channel=True,
+                                  running_gptq=False)
+        self.assertTrue('The HSE error method for parameters selection is only supported when running GPTQ '
+                        'optimization due to long execution time that is not suitable for basic PTQ.' in e.exception.args[0])
 
     def test_threshold_selection_hmse_no_kernel_attr(self):
         def _generate_bn_quantization_tpc(quant_method, per_channel):
@@ -258,8 +225,9 @@ def _generate_bn_quantization_tpc(quant_method, per_channel):
                                                         n_samples=1,
                                                         target_nodes=[node])
 
-        with self.assertRaises(ValueError, msg='Not enough hessians are cached to fulfill the request') as e:
+        with self.assertRaises(ValueError) as e:
             self.his.fetch_hessian(expected_hessian_request)
+        self.assertTrue('Not enough hessians are cached to fulfill the request' in e.exception.args[0])
 
 
 if __name__ == '__main__':